joint CASUS Institute Seminar, Janina Schreiber and Gentian Zavalani, Center for Advanced Systems Understanding CASUS, Helmholtz-Zentrum Dresden-Rossendorf (HZDR)
Abstract of the talk // Janina Schreiber // Optimization tasks arise in many fields of applications, ranging from analyzing and adjusting simulations of complex systems across all disciplines to inferring optimal neural network architectures. Black box optimization methods specifically, are designed to find an optimum without any a priori knowledge of the underlying function by sampling the objective function as sparsely as possible, and cover a wide range of optimization tasks.
In this talk Janina will introduce the Polynomial-Model-Based Optimization (PMBO), a novel black box optimization technique motivated by Bayesian optimization. The optimization model generated by PMBO is iteratively updated according to an acquisition function that balances the exploitation and exploration rate. The location of the desired optimum is predicted by efficiently computing the optimum of the (analytic, polynomial) optimization model.
Abstract of the talk // Gentian Zavalani // In this talk, Gentian introduces a novel high-order integration method for surface integrals. The approach rests on curved triangulations, approximating a vast class of regular (smooth) surfaces. The novelty of his contribution is given by accurate interpolation of the closest point projection, realizing the curved triangles. To this end, Gentian and his colleagues incorporate recent advances in multivariate interpolation, suppressing Runge’s phenomenon when interpolating the closest point projection in proper chosen, transformed Chebyshev-Lobatto nodes. The specific transformation proposed in this process leads the integration scheme to be largely independent of the mesh quality and to remain stable even at high orders.
Further, Gentian and his team combine their technique with the novel global polynomial level set parametrization method (GPLS). GPLS only requires regular samples P ⊆M of the surface M in order to derive implicit global models of the surface M=Q_{M}^{-1}(0). This allows them to apply their high-order integration scheme to a vast class of non-parameterized surfaces by deriving the closest point map from the global polynomial level set. As their empirical demonstrations suggest, Gentian and his colleagues expect the approach to be applicable for a broad class of computational tasks in numerical differential geometry arising for “real world” problems across disciplines, e.g., bio-physics, material sciences and computer graphics.
Janina and Gentian will be talking live in Görlitz. However, as the event is organized in a hybrid format that includes a videoconferencing tool by Zoom Inc., people interested in the topic have the chance to also join the talk remotely. Please ask for the login details via contact@casus.science.